Evolution of the interfaces in a two dimensional Potts model

Invariance principle for a Potts interface along a wall

We consider nearest-neighbor two-dimensional Potts models, with boundary conditions leading to the presence of an interface along the bottom wall of the box. We show that, after a suitable diffusive scaling, the interface weakly converges to the standard Brownian excursion.

低温三维Ising与Potts界面在硬底板上方的对数离域性

Logarithmic delocalization of low temperature 3D Ising and Potts interfaces above a hard floor

该研究针对带硬底板边界的三维低温Ising和Potts模型，证明界面熵排斥可克服底板吸引作用，得到界面高度对数发散下界及推测紧上界，填补了Potts模型相关结果空白。

三维 Potts 界面的极值

Extrema of 3D Potts interfaces

本文研究三维 Potts 与 FK 模型界面的全局极值，证明四类极值由不同大偏差速率及常数控制，并发展新方法克服 Potts 模型缺乏单调性的困难。

二维 Potts 模型中的不连续相变：I. 有序-无序界面的收敛性

Discontinuous transition in 2D Potts: I. Order-Disorder Interface convergence

本文研究 q > 4 时二维 Potts 模型在有序-无序边界条件下的界面，证明其具有 $\sqrt{N}$ 涨落并收敛于 Brownian 桥，方法基于 FK-percolation、six-vertex 模型与 Ashkin-Teller 模型随机团簇表示的耦合。

Lectures on the Ising and Potts models on the hypercubic lattice

Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids (lattice gases). It has been understood since the 1980s that random geometric representations, such as the random walk and random current representations, are powerful tools to understand spin models. In addition to techniques intrinsic to spin models, such representations provide access to rich ideas from percolation theory. In recent years, for two-dimensiona…

Non-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces

We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble CLE$_{κ'}$ for $κ'$ in $(4,8)$ that is drawn on an independent $γ$-LQG surface for $γ^2=16/κ'$. The results are similar in flavor to the ones from our paper dealing with CLE$_κ$ for $κ$ in $(8/3,4)$, where the loops of the CLE are disjoint and simple. In particular, we encode the combined structure of the LQG surface and the CLE$_{κ'}$ in terms of stable growth-fragmentation trees or their variants, which also appear in the asymptotic study of peeling processes on d…